The development of multi-scale computational tools to model multiple hydraulic fractures propagating in complex media.

过去十年，全球能源格局发生了重大变化，这在很大程度上要归功于一种通常被称为“水力压裂”的工艺，这种工艺使从页岩气藏中提取碳氢化合物在经济上是可行的。这一过程是由一项新技术实现的，该技术使水平井产生多条水力裂缝(HFs)成为可能。虽然水力压裂技术一直备受争议，但由于碳氢化合物泄漏到地下水的风险，这项新技术也可以通过在地热储层中创建裂缝网络来产生更清洁的能源。由于地壳顶部10公里处蕴藏的能源是所有石油和天然气储量的5万倍，这项创新技术在生产清洁能源方面也具有巨大的潜力。为了将水力压裂的环境风险降到最低，并优化HF的放置，有必要拥有能够模拟这些新的演化HF构型的设计工具。然而，高频技术的这些重要发展使现场实践超出了目前的计算机模拟工具的范围。现有的工具主要集中在模拟单个高频在分段均匀弹性介质中的传播过程。现在需要的是模拟多个高频同时在复杂的固体介质中传播并与预先存在的节理和断层相互作用的能力。*即使是单一高频在均匀弹性介质中传播的最简单的数学模型也涉及具有复杂多尺度结构的退化的非线性积分-偏微分方程组的耦合系统。这些方程还涉及一个奇异的自由边界问题，在该问题中，前沿速度只能通过评估一个可区分的极限来确定。这种奇异的自由边界问题限制了高频模拟器对高频的模拟，高频的传播由单一的物理过程控制--通常是岩石破裂时释放的能量。在最近的一项重大突破(Peirce&Detournay，2008)中，我们发展了一种稳健而精确的数值方法，它使用局部分析得到的尖端渐近解来完全解决这类奇异自由边界问题。我们称这个方案为隐式水平集算法(ILSA)，我们已经用它来解决一些公开问题。*该提案概述了一项雄心勃勃的研究计划，该计划利用创新的ILSA计划进一步开发一套新颖的计算工具，使工程师能够在优化碳氢化合物生产的同时将水力压裂对环境的影响降至最低。这项研究计划已经引起了工业界的关注，并将为该领域的石油工程师提供新技术。建立这些强大的设计工具可能会导致监管要求设计HF处理，以实现最大限度地使用最少的水开采天然气。这对政策的潜在影响是相当大的。**

The past decade has seen a significant change in the global energy landscape, largely due to a process commonly known as "fracking" that has made the extraction of hydrocarbons from shale gas reservoirs economically viable. This process has been enabled by a new technology that makes possible the generation of multiple hydraulic fractures (HFs) from horizontal wells. While fracking has been controversial, due to the risk of hydrocarbons leaking into groundwater, this novel technology can also be used to generate cleaner energy by creating fracture networks in geothermal reservoirs. Since the top 10 km of the earth's crust holds 50,000 times as much energy as all oil and gas reserves, this innovative technology also has huge potential for generating clean energy. To minimize the environmental risk of fracking and to optimize the placement of HF, it is necessary to have design tools that can simulate these new configurations of evolving HF. However, these important developments in HF technology have put field practice beyond current computer simulation tools. Existing tools are primarily focused on simulating the evolution of a single HF propagating in a piece-wise homogeneous elastic medium. What is now required is the capacity to simulate multiple HF that simultaneously propagate in complex solid media and interact with pre-existing joints and faults.***   Even the simplest mathematical model for a single HF propagating in a homogeneous elastic medium involves a coupled system of degenerate nonlinear integro-partial differential equations with a complex multi-scale structure. These equations also involve a singular free boundary problem, in which the front velocity can only be determined by evaluating a distinguished limit. This singular free boundary problem has limited HF simulators to the modeling of HF whose propagation is governed by a single physical process - typically the energy released when breaking the rock. In a recent significant breakthrough (Peirce & Detournay, 2008), we developed a robust and accurate numerical technique that uses the tip asymptotic solution obtained by local analysis to completely resolve this class of singular free boundary problem. We called this scheme the Implicit Level Set Algorithm (ILSA), which we have already used to solve a number of open problems. ***   This proposal outlines an ambitious research program that leverages the innovative ILSA scheme to further develop a novel set of computational tools that will enable engineers to optimize hydrocarbon production while minimizing the environmental impact of fracking. This program of research has already attracted the attention of industry and will provide new technology to petroleum engineers in the field. Establishing these robust design tools may result in regulatory requirements to design HF treatments to achieve maximal gas extraction using the least water. The potential impact for policy is considerable.**